Perspective line generator

ABSTRACT

A perspective line generator or drafting instrument to aid in preparing accurate perspective views of objects using a small drawing surface where the vanishing points are too remote from the drawing surface to achieve same by conventional techniques with a T-square or straight edge. The generator consists of a specially constructed T-shaped drawing arm having a chordal head attached to one end thereof and a guide comprised of two or more articulated chordal segments of identical size and shape as the chordal head. The segments may be connected together by one plane of selected construction. The segments may be secured to a flat drawing surface to provide a continuous guide for the head of the drawing arm. When suitably articulated, they will position the drawing arm so that it is disposed to produce lines that converge toward a common center or vanishing point.

United States Patent 11 1 1111 3,868,777

Bell Mar. 4, 1975 PERSPECTIVE LINE GENERATOR [76] inventor: Franklin D. Bell, P.O. Box 14. Pm'mry E'\'am"er llarry Harman Eatomown, 07724 Attorney, Agent, or firm-Lucke & Lucke [22] Frled: Feb. 2, 1973 [57] ABSTRACT [2]] Appl 329l32 A perspective line generator or drafting instrument to aid in preparing accurate perspective views of objects [52] U.S.Cl. 33/77 using a small drawing surface where the vanishing [51] Int. Cl. B43l 13/14 points are too remote from the drawing surface to [58] Field of Search 33/77; 16/150; 308/2 A achieve same by conventional techniques with a T- square or straight edge. The generator consists of a [56] References Cited specially constructed T-shaped drawing arm having a UNITED STATES PATENTS chordal head attached to one end thereof and a guide 1.122.533 12 1914 0 '1 l or more "tlculated Chordal M68353 $1916 ig; ments of ldentlcal size and shape as the chordal head.

1.245.539 11/1917 Wagner 33/117 The Segments may be connected together y One 1.390.181 9/1921 Van Etten 33/99 Plane of selected construction- 2 524.990 10/1950 Randolph 33/77 T Q 2 768,444 lO/l956 Gaut et al. 33/77 iggg f l i f r g g ifi 3 159.918 12/1964 015611 et =11 33/77 e a muous. e f e ea 0 3 437 7/1965 Schilling 16/150 drawing arm. When su1tably artlculated, they wrll 33301430 l/l967 Cornelius:::::::: 16/150 Posmo the drawing arms) that it is disposed 3.450.410 6/1969 Castagna 274/23 R P lines Converge towatd a common Center or vanishing point.

7 Claims, 11 Drawing Figures PMENTEU 41975 Mb. NM wm 9mm Pf -JENTED 419-75 3.868.777

sum a g 1 FIG. IO

FATENTEU 4W5 LVP SHEET Work-Surface RVP W Example No.1

Work Surface Drcwlng Edge Articulated Cho'rdol Guide Segment No.1

EXGmp le No.2

FATENTEW 3.868.777

W vp ork Surface RVP Artieoloted Chordol Guide Segment No.2 Drawing Arm Chordol Heod Ar'ticulofed Chordol Gulde Segment No.1

Example No.5

Work Surface F Horizon I -Ch'o rdol/ Gulde Segment No.2

Example No.4

PATENTED 419-75 SHEET 7 Work Surface 7 vvP Chordol Guide Segments RVP lBlSECTOR I PT-AA InsefA PERSPECTIVE LINE GENERATOR BACKGROUND OF THE INVENTION 1. Field of the Invention This invention relates to drafting instruments which aid in the production of perspective drawings, especially where the vanishing points thereof are located beyond the drawing surface.

2. Description of the Prior Art Many attempts have been made to provide a convenient means for producing perfect architertural perspective drawings and the like, where it is common for vanishing points to be far removed from the actual drawing surface per se, but all have so far failed to reach this desirable objective.

Examples of prior art devices are shown in the following patents:

1,969,758 8/I4/34 McCoy 2,768,444 /30/56 Gaut et al. 2.876547 3/10/59 Spencer et al. 3,159,918 IZ/ 8/64 Olson et al.

The prior art does not allow the flexiblity and range necessary to accomodate an unrestricted number of vanishing point locations and an unlimited number of picture sizes while using a single, compact simple device. Prior straight-edged guide devices limit both vanishing point location and drawing size. For instance, Olson pivots the outer ends of his guide arms upon a base plate so that he can move the arms with respect to the T-square head only a very limited amount thus restricting both the possible vanishing point locations and the size of the drawing. He makes no attempt, nor will his configuration permit it, to relate the length of his arms to the T-square head.

The remainder of the known prior art use either partial curves or curves added together, but this technique also limits the location of the vanishing point this time to the center of the generated curve and further requires extensive mathematical computation to determine the correct curve placement with respect to the intended perspective drawing.

None of the prior art is capable of accomplishing the extensive results possible with the generator herein disclosed.

SUMMARY OF THE INVENTION The perspective line generator consists ofa new form olguide in which a plurality of contiguous articulatable chordal segments having the same length form a continuous guide edge for cooperation with a specially constructed drawing arm having a transverse head of identical dimensions to those of said segments. This new form of guide can accommodate any length of chordal segment provided the drawing arm has an identically shaped head as the segments with which it is to be used.

The segments may be connected along one side thereof by a form of bendable membrane or by two curves or the like, wherein the joint or axis of articulation lies in one and the same plane, thus producing a continuous guide edge without indentation or protrusion for smooth cooperation with the chordal head.

This instrument is intended for use in the preparation of perspective drawings where the use of vanishing points is required. It can also be used in the preparation of other three-dimensional representational forms of drawing, such as isometric, dime'tric or trimetric pro jection drawings.

BRIEF DESCRIPTION OF THE DRAWINGS Further features and advantages of the invention will be apparent in the following detail description and the accompanying drawings which illustrate preferred embodiments of the invention, wherein FIG. 1 is a top plan view of a T-shaped drawing arm with alternate drawing edges. A transverse chordal head is connected by a bridge member to the arm at one end thereof;

FIG. 2 is a side elevation or an edge view of the drawing arm shown in FIG. I used in conjunction with a straddled a chordal segment;

FIG. 3 is an enlarged cross-sectional view of the drawing arm showing the realtionship of the work surface to it and the chordal head, as taken on line 3-3 of FIG. 1;

FIG. 4 is a semi-diagrammatic showing of the drawing arm used with two or three chordal segments of a guide to produce multiple lines leading to a common center point. At the left, the chordal head contacts the chordal segments on the inside of a projected. are around the drawing surface, whereas at the right the T- shaped device is used in reversed position with the bridge member overlying the chordal segments:

FIG. 5 is a top plan view of two articulated chordal segments integrally joint together at one end;

FIG. 6 is a side elevation of the three contiguous chordal segments of FIG. 5 shown in juxtaposed position and joined by a smooth one plane connection.

FIG. 7 is a top plan view of a one plane connection between two chordal segments shown in aligned position in solid line and in articulated position in dotted line, taken on line 77 of FIG. 6;

FIG. 8 is a top plan view of an arcuate one plane hinge with two aligned segments shown joined together in solid line with one segment shown articulated in dotted line;

FIG. 9 is an edge view of the solid line segments shown in FIG. 8;

FIG. 10 is an enlarged exploded view, partly broken away, of two juxtaposed chordal segments with the hinge in closed position such as shown in FIGS. 8 and 9;

FIG. 11 is an exploded view of a further modification of the two juxtaposed chordal segments joined by an alternate arcuate hinge; and

Examples numbered 1-8 illustrate method steps of using this drawing instrument to achieve various perspective drawings having remote vanishing points.

DESCRIPTION OF A PREFERRED EMBODIMENT FIGS. 1-3 show a specially constructed T-shaped drawing device generally designated 50 consisting of a longitudinal parallel edge drawing arm 51 attached to a transverse parallel edge chordal head 52 at the center thereof by a T-shaped bridge member 53 mounted as by screws 54 to the top surface of the head and of the arm 51 at a point spaced from the head to form a raised bridge portion 60. The head is provided with squared ends and two pairs of guide contact points 52a, 52b and 52c, 52d. As seen from FIG. 3, both sides of the arm 51 contact the work surface 55 and form alternate orselective drawing edges 56 contiguous with the drawing surface.

The under side of the head is provided with an antiskid element 57 at each end which may be adhered by cement or secured through a hole in the head by a holding screw 58.

Two or more of the chordal segments 59a, 59b,59c may be used jointly with the T-shaped drawing device as illustrated. The shape and dimensions of each parallel edged, square ended chordal segment is identical to the head 52 as seen in FIG. 4. This is a most important feature in many respects, one of which is illustrated on the right hand side of FIG. 4. Here two segments 59a,

% are shown insterted under the bridge portion 60 of the T-shaped device 50, the bridge portion being raised the precise distance by the underlying head 52 and arm 51 to clear the segments. In this instance the arm is facing away from the vanishing point so that the two inner drawing arm guide points 52c, 52d are used in conjunction with segments 59a, 59b...The left-hand side of FIG. 4 shows an alternate position with the drawing arm projecting toward the vanishing point. The head is again used in conjunction with two or more segments 59a, 5% using the two outer guide points 52a, 52 b. The bridge portion 60 of the drawing arm does not pass over or straddle the segments in this case. In either instance lines drawn along either the solid or dotted line showing of drawing edge 56 will lead to the right vanishing point 61. It is noted that further radial lines 62, formed by moving the device 50 around a continuous arcuate guide edge of adjoining segments, all converge on point 61 of the guide edge.

It isnt necessary to pre-determine the arc. The are will be a natural result of the placement of the chordal guide segments when the drawing arm is aligned with any two lines that have been determined by the artist to have the desired convergence. The so placed segments will enable the artist to draw any number of lines that will also converge toward the same point within the range allowed by the length of the guide segment. The range can be extended by using additional guide segments.

The dimentionless hinge joints between two or more of the chordal segments are described herein as one plane joints, wherein the actual center of the hinge is located at. the joint. It is a hinge in which its apex or center lies in the same plane as its surface, i.e., it has no hinge pin or offset pivot. This can be effected by a strip of membrane such as paper, adhesive tape, etc. being adhered to one side of a series or plurality of contiguous segments forming the articulatable guide as well as the polypropylene and annular means of connection illustrated herein.

The enlarged pair of hinged otherwise joined segments 59a, 59b, 59c shown in FIG. 5 shows their con struction in greater detail and one means of joining them together. The segments and their, one plane hinges 63 may be made of any bendable membrane or plastic such as one of a group of polyolefin plastics which have been found to posses self-hinging characteristics to an extraordinary degree, and is extremely strong in very thin sections. In this instance it forms an almost paper thin centerless hinge capable of constant flexing without breakage.

Alternately, two or more segments could be formed from a continuous strip of polyproylene suitable slotted to provide one plane hinging at the chordal length matching the chordal head of the drawing arm.

It will seen from FIG. 7 that the one plane hinge 63 will not produce protrusions or indentations at point where the guide edges of adjoining chordal guide segments meet as a result of the flexure of the one plane hinge 63 and will even allow the said guide edges of adjoining chordal segments to come into complete contact along their entire length when flexed 180.

It will be seen from FIG. 5 that the non-protruding hinge 63 allows the dotted line showing of the straight edge head 52 to lie flush against the straight edge ofthe segment 59a from guide points 52a to 521) and thus permit exact projection along its drawing arm 51 and drawing edge 56. This is one of the more important advantages of the invention and overcomes the difficulties of the prior art. The alternate dotted line showing of head 52 has its guide point 52a contacting segment 59a and its guide point 52!) contacting segment 59b'in position to line up another radial line similar to the projections 62 in FIG. 4.

It will be seen from FIG. 5 that when the guide edges of adjoining segments are aligned in the fully extended position there appears to be a space as shown between segments 59b, 59c. This is the slot 64 used to create the one plane hinge 63 as shown in FIG. 7.

FIGS. 8 and 9 show another means of obtaining a one plane hinging of segments 59d, 592 by the arcuate hinge shown in FIG. 10. This hinge consists of a flat semi-circular plate 76 which fits into two quartercircular recesses 77, 77' of segments 59d, 59e. Each hinge plate 76 is provided with a spreading resilient element 78 at each end of its lower surface. These elements are insertable into and retained by frictional contact with arcuate slots 79, 79 in their corresponding recesses lt will be seen that when the plate is positioned within its recess, the two segments may be articulated to any desired degree from 180, as illustrated in dotted lines in FIG. 8, and retained in such position by elements 78. r

The modified hinge shown in FIG. II has a slotted semi-circular plate 80 which fits into two complementary quarter circular recesses 81, 81' to receive the pins 85. Each of the pins have a slotted head 86 and a depending collar 87 for frictional contact with bevelled edges 83. It will be seen that this hinge works on the same principle as that shown in FIG. 10, i.e., the segments 59f, 59g may be articulated to the desired degree as shown in FIG. 8 and retained in said position by pins which are free to rotate within slots 82. Pins 85 are here shown as slotted screws.

Regardless of the type of hinge selected from those illustrated in FIGS. 5-7, 8-10 or 11, all are centerless and create no obstruction or offset which would prevent continuous contact points 5211, 52h, 52c, 52d of head 52 and therefore true perspective projection of the drawing edge to one or more common vanishing points.

On each end of the chordal segments 59a, 59b, 590 a round button 66 has been punched from its respective segment. The segment may be secured in proper position to a drawing board or work surface 55, see FIGS. 5 and 6, by pushing a drawing pin or thumb tack 72 through a hole 67 in the center of each button to prevent dislocation during the drawing process. An adhesive disk or paper 68 can also be used to prevent marring the drawing surface 55.

Referring now to Examples 1-8 which illustrate some of the progressivesteps of preferred methods of using the perspective line generator to initially draw or trueup the perspectives of a free hand drawing. Example 1 shows a work surface with a right vanishing point RVP, a left vanishing point LVP and a vertical vanishing point VVP all located beyond the confines of the work surface upon which the drawing is to be made. Lines AB, C-D, E-F and G-H constitute a set of arbitrarily established lines, portions of which will form part of a finished perspective drawing.

The next step is shown in Example No. 2. Here one of the drawing edges of the drawing arm is aligned with line A-B at any convenient point so that this drawing edge will sweep the area upon which the perspective drawing will be made. Then a chordal guide segment No. l is affixed to the work surface in juxtaposition to the inner surface of the chordal head so that the ends of the chordal guide segment and the chordal head are aligned.

In Example No. 3, one of the drawing edges of the drawing arm is aligned with line C-D so that a chordal head guide point is in contact with the outer edge of the chordal segment No. 1. Then chordal guide segment No. 2 is joined to chordal segment No. l at point X as by a centerless hinge and articulated until its outer edge is in contact with the chordal head, and then affixed to the work surface in this position. All lines drawn along this drawing edge when the guide points of the chordal head are in contact with the edges of chordal guides Nos. 1 and 2 will terminate in the right vanishing point RVP.

The next sequential Example No. 4 shows the end result of performing the following steps: Draw line J-K perpendicular to line 6-H and crossing lines C-D and E-F. Draw line L-M through the intersection of C-D and J-K parallel to line 6-H and crossing line A-B. Draw line P-Q through the intersection of L-M and A-B parallel to J-K. Draw line N-O through intersection of E-F and J-K parallel to 6-H and crossing line PQ. Draw line R-S through the intersections of lines GH, AB and NO, P-Q. Lines R-S and E-F will terminate at vanishing point LVP. The perspective horizon will lie on a line connecting LVP and RV? that is also perpendicular to the extension of line G-l-l.

in Example No.5, chordal guide segments Nos. 3 and 4 are located and affixed to the drawing surface in a similar manner to segments 1 and 2 as described in Examples 1-3. All lines drawn along the drawing edge when the guide points of the chordal head are in contact with the edges of chordal guides Nos. 3 and 4 will terminate in vanishing point LVP.

lfvanishing point VVP is at infinity all verticals in the perspective drawing will be parallel to G-H. This is typical of two point" perspective drawings. Chordal guide segments 5, 6, 7 and 8 can be affixed to the drawing surface to provide a guide for the chordal head I when drawing. such vertical lines.

To draw the line T-U and complete the perspective drawing shown in Example No. 6, an additional chordal segment will be needed, otherwise the drawing edge of the drawing arm will not sweep that far using only chordal segments 1 and 2. This is accomplished by performing the construction steps shown in broken lines. Connect the intersections of (1-H and-AB with the intersections of CD and L-M. Connect the intersections of CD and L-M. Connect the intersections of A-B and L-M with the intersections of C-D and 6-H. Draw a dotted vertical line parallel to G-H through the intersecting diagonals that cross line C-D. Draw a line from the intersection of 6-H, A-B through the intersection ofthis vertical and C-D to cross line L M. In a like manner draw a line from the intersection of L-M, A-B through the intersection of this vertical and C-D that crosses G-H. Line V-W drawn through these last mentioned intersections will terminate in vanishing point RVP. Line V-W is used to position guide segment No. 9.

Using the techniques already described, affix chordal guide segment No. 9 to the drawing surface. Line T-U can now be drawn to complete the perspective drawing of a rectangular object. As will be seen from Example 6 the drawing arm will not sweep through line TU until segment 9 is added.

In Example No. 7, line X-Y and lineG-H terminate at vanishing point VVP. This condition exists in three point perspective. Chordal guide segments 10, 11 and 12 are affixed to the work surface using techniques previously described. The dotted line position of the T- square device is used in a similar way to that used in Example 6 to locate segment 9. In this case it is used to position segment 12. All lines drawn along the drawing edge when the guide points of the chordal head are in contact with the edges of the chordal guide segments 10, 11 and 12 will terminate in vanishing point VVP.

The method of establishing measuring points and scale for two point perspective is shown in Example No. 8. Points AA and BB are the intercepts of the bisectors of the perspective angles formed by the intersection of lines E-F, C-D and RS, A-B respectively, located on lines JK and PQ respectively. The construction is shown in inset A. Lines drawn through these intercepts from apex of their respective angles will terminate at measuring point HMP, which also lies on the horizon line.

in effect the measuring pointv HMP is the vanishing point for the diagonal of a square in the horizontal plane. A scale for measuring can be constructed using a suitable ratio of vertical measure to horizontal measure. Such a scale may then be used to construct an accurate perspective drawing of any subject matter.

Some of the important features of this invention are:

1. It permits drawing radiating lines that converge toward a vanishing or center point located beyond the working surface.

2. The location of the vanishing or center point can be anywhere up to and including infinity.

3. The articulated guide segments can be located at any convenient position on the drawing surface.

4. A separate articulated guide segment can be used to accommodate each of several vanishing points.

5. The articulated guide segment can be extended to accommodate any degree of angular are about the vanishing or center point.

6. The guide segment can be attached directly to the drawing surface.

7. There is no mechanical adjustment necessary.

8. Only one drawing arm is required regardless of the number of center points being used.

9. Guide segments can be removed, repositioned or replaced without losing accuracy and any number can be used.

10. Any center point can be accommodated from within the working area or surface.

1 l. A minimum working surface is all that is needed when using this perspective line generator.

12. It uses a special T-shaped device in' a different way and no mathematics are involved.

The forms of the invention here described and illustrated are presented merely as examples of how the invention may be embodied and applied. other forms, embodiments and applications of the invention will suggest themselves to those skilled in the art.

I claim:

I. A perspective line generator comprising a guide of articulatable chordal segments of equal length used in conjunction with a drawing arm attached to a transverse chordal head, said head having identical dimensions to those of said segments, a contiguous plurality I of said articulatable chordal segments forming a smooth continuous guide edge, said guide and said drawing arm cooperating to produce converging lines when the head of said arm is placed at various points of contact with said continuous guide edge when said chordal segments are articulated to positions other than in a straight line, means for articulating said segments to each other to form said continuous guide edge and wherein said means comprises a flexible membrane attached to said segments to form part of said continuous guide edge.

2. A generator according to claim 1, wherein either side of said chordal head can be used in conjunction with said guide edge.

3. A generator according to claim 2, wherein a bridge member connects said arm to said head allowing said drawing arm to straddle said guide for cooperation of the other side of said head with said guide edge.

4. A generator according to claim 1, wherein said guide is prepared fro from polypropylene.

5. A perspective line generator adapted for use on a working surface comprising a T-square having a longitudinal parallel-edged drawing arm and a transverse parallel-edged chordal head with squared ends in combination with a guide consisting of at least two paralleledged chordal segments having like dimensions and shape as said chordal head, means for pivotally joining said segments at abutting ends to form a continuous guide edge comprising complementary circular recesses at each abutting end forming a continuous semicircular recess with its ends opening into said continuous guide edge and its center positioned at abutting corners which include said guide edge, each of said recesses provided with an arcuate slot intermediate the length thereof, and a flat arcuate plate adapted to fit into said complementary recesses, a resilient expanding tudinal parallel-edged drawing arm and a transverse parallel-edged chordal head with squared ends in combination with a guide consisting of at least two paralleledged chordal segments having like dimensions and shape as said chordal head, means for pivotally joining said segments at abutting ends to form a continuous guide edge comprising complementary circular recesses at each abutting end forming a continuous semicircular recess with its ends opening into said continuousguide edge and its center positioned at abutting corners which include said guide edge, each of said recesses provided with a pin hole intermediate the width thereof proximate the end of each said segment, and an arcuate plate adapted to fit into said complementary recesses, an arcuate slot disposed at both ends of said plate, a pin adapted to be inserted through each of said slots into each of said holes to enable said segments to be articulated about said plate to a predetermined position said head cooperating with said guide to produce converging lines when said guide is pivoted to angular portions.

7. A perspective line generator adapted for use on a working surface comprising a T-square having a longitudinal parallel-edged drawing arm and a transverse parallel-edged chordal head with squared ends in combination with a guide consisting of at least two paralleledged chordal segments having like dimensions and shape as said chordal head, means for pivotally joining said segments at abutting ends to form a continuous guide edge comprising complementary circular recesses at each abutting end forming a continuous semicircular recess with its ends opening into said continuous guide edge and its center positioned at abutting corners which include said guide edge, a flat arcuate plate adapted to mate with said semicircular recess, said plate and segments having means thereon to maintain said segments in pivotally joined relationship, said head cooperating with said guide edge to produce converging lines when said guide is arranged to angular positions. 

1. A perspective line generator comprising a guide of articulatable chordal segments of equal length used in conjunction with a drawing arm attached to a transverse chordal head, said head having identical dimensions to those of said segments, a contiguous plurality of said articulatable chordal segments forming a smooth continuous guide edge, said guide and said drawing arm cooperating to produce converging lines when the head of said arm is placed at various points of contact with said continuous guide edge when said chordal segments are articulated to positions other than in a straight line, means for articulating said segments to each other to form said continuous guide edge and wherein said means comprises a flexible membrane attached to said segments to form part of said continuous guide edge.
 2. A generator according to claim 1, wherein either side of said chordal head can be used in conjunction with said guide edge.
 3. A generator according to claim 2, wherein a bridge member connects said arm to said head allowing said drawing arm to straddle said guide for cooperation of the other side of said head with said guide edge.
 4. A generator according to claim 1, wherein said guide is prepared fro from polypropylene.
 5. A perspective line generator adapted for use on a working surface comprising a T-square having a longitudinal parallel-edged drawing arm and a transverse parallel-edged chordal head with squared ends in combination with a guide consisting of at least two parallel-edged cHordal segments having like dimensions and shape as said chordal head, means for pivotally joining said segments at abutting ends to form a continuous guide edge comprising complementary circular recesses at each abutting end forming a continuous semi-circular recess with its ends opening into said continuous guide edge and its center positioned at abutting corners which include said guide edge, each of said recesses provided with an arcuate slot intermediate the length thereof, and a flat arcuate plate adapted to fit into said complementary recesses, a resilient expanding element projecting downwardly from each end of said plate, said elements adapted to frictionally fit into said slots to enable said segments to be articulated about said plate to a predetermined position said head cooperating with said guide to produce converging lines when said guide is pivoted to angular portions.
 6. A perspective line generator adapted for use on a working surface comprising a T-square having a longitudinal parallel-edged drawing arm and a transverse parallel-edged chordal head with squared ends in combination with a guide consisting of at least two parallel-edged chordal segments having like dimensions and shape as said chordal head, means for pivotally joining said segments at abutting ends to form a continuous guide edge comprising complementary circular recesses at each abutting end forming a continuous semi-circular recess with its ends opening into said continuous guide edge and its center positioned at abutting corners which include said guide edge, each of said recesses provided with a pin hole intermediate the width thereof proximate the end of each said segment, and an arcuate plate adapted to fit into said complementary recesses, an arcuate slot disposed at both ends of said plate, a pin adapted to be inserted through each of said slots into each of said holes to enable said segments to be articulated about said plate to a predetermined position said head cooperating with said guide to produce converging lines when said guide is pivoted to angular portions.
 7. A perspective line generator adapted for use on a working surface comprising a T-square having a longitudinal parallel-edged drawing arm and a transverse parallel-edged chordal head with squared ends in combination with a guide consisting of at least two parallel-edged chordal segments having like dimensions and shape as said chordal head, means for pivotally joining said segments at abutting ends to form a continuous guide edge comprising complementary circular recesses at each abutting end forming a continuous semi-circular recess with its ends opening into said continuous guide edge and its center positioned at abutting corners which include said guide edge, a flat arcuate plate adapted to mate with said semicircular recess, said plate and segments having means thereon to maintain said segments in pivotally joined relationship, said head cooperating with said guide edge to produce converging lines when said guide is arranged to angular positions. 